computeVAB {TDAvec} | R Documentation |
A Vector Summary of the Betti Curve
Description
For a given persistence diagram ,
computeVAB()
vectorizes the Betti Curve
where the weight function
Usage
computeVAB(D, homDim, scaleSeq)
Arguments
D |
matrix with three columns containing the dimension, birth and death values respectively |
homDim |
homological dimension (0 for |
scaleSeq |
numeric vector of increasing scale values used for vectorization |
Value
A numeric vector whose elements are the average values of the Betti curve computed between each pair of
consecutive scale points of scaleSeq
=:
where
Author(s)
Umar Islambekov, Hasani Pathirana
References
1. Chazal, F., & Michel, B. (2021). An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists. Frontiers in Artificial Intelligence, 108.
2. Chung, Y. M., & Lawson, A. (2022). Persistence curves: A canonical framework for summarizing persistence diagrams. Advances in Computational Mathematics, 48(1), 1-42.
Examples
N <- 100
set.seed(123)
# sample N points uniformly from unit circle and add Gaussian noise
X <- TDA::circleUnif(N,r=1) + rnorm(2*N,mean = 0,sd = 0.2)
# compute a persistence diagram using the Rips filtration built on top of X
D <- TDA::ripsDiag(X,maxdimension = 1,maxscale = 2)$diagram
scaleSeq = seq(0,2,length.out=11) # sequence of scale values
# compute vector of averaged Bettis (VAB) for homological dimension H_0
computeVAB(D,homDim=0,scaleSeq)
# compute vector of averaged Bettis (VAB) for homological dimension H_1
computeVAB(D,homDim=1,scaleSeq)